The Daily Mail says Bayern have earmarked the pair as potential transfer targets but both are also wanted by Arsene Wenger.
Gotze scored Borussia Dortmund's winner against Munich on Saturday.
Reus, 22, who scored a hat-trick in Borussia Moenchengladbach's 5-0 demolition of Werder Bremen, has also captured Bayern's attention.
"Gotze is a magnificent player despite being only 19 years old. Of course we observe such players," Bayern chief Karl-Heinz Rummenigge told Sunday newspaper Welt am Sonntag.
"Reus has a clause in his contract that isn't exactly cheap (but) he could give us even more quality in the long run."